I tried to optimize the web build for most phones also, but I guess it just doesn't work on all devices for now. A dedicated mobile release is planned later, until that I'm afraid there is not much that can be done...
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I managed a workaround for this issue by forcing the browser to be rendered at 16:9 in the Full Screen Apps setting.
It's very hard to read the stats difference when you're dragging a new item to a dwarf because your finger is in the way, so using an S-Pen is recommended.
Is there anything you can do about the music? Even if I switch tabs on PC or the phone screen locks the music keeps playing full blast. It should probably mute when the tab loses focus.